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Let phi(t) be the characteristic function, defined as the Fourier transform of the probability density function P(x) using Fourier transform parameters a=b=1, phi(t) = ...

Based on a problem in particle physics, Dyson (1962abc) conjectured that the constant term in the Laurent series product_(1<=i!=j<=n)(1-(x_i)/(x_j))^(a_i) is the multinomial ...

The exponential transform is the transformation of a sequence a_1, a_2, ... into a sequence b_1, b_2, ... according to the equation ...

Let C=C^+ union C^- (where C^+ intersection C^-=emptyset) be the disjoint union of two finite components C^+ and C^-. Let alpha and beta be two involutions on C, each of ...

Let (a)_i be a sequence of complex numbers and let the lower triangular matrices F=(f)_(nk) and G=(g)_(nk) be defined as f_(nk)=(product_(j=k)^(n-1)(a_j+k))/((n-k)!) and ...

A graceful permutation sigma on n letters is a permutation such that {|sigma(i)-sigma(i+1)|:i=1,2,...,n-1}={1,2,...,n-1}. For example, there are four graceful permutations on ...

An orientation of an undirected graph G is an assignment of exactly one direction to each of the edges of G. Only connected, bridgeless graphs can have a strong orientation ...

A set of generators (g_1,...,g_n) is a set of group elements such that possibly repeated application of the generators on themselves and each other is capable of producing ...

A two-dimensional generalization of the Haar transform which is used for the compression of astronomical images. The algorithm consists of dividing the 2^N×2^N image into ...

Let the values of a function f(x) be tabulated at points x_i equally spaced by h=x_(i+1)-x_i, so f_1=f(x_1), f_2=f(x_2), ..., f_7=f(x_7). Then Hardy's rule approximating the ...